I open my eyes Saturday morning to see a drab green blur. The blur turns out to be my son, Dave, dressed in his Boy Scout uniform. He is shaking my arm. "Davey, what are you doing here?" I ask. He says, "Dad, it's seven o'clock! "Seven o'clock? I'm trying to sleep. Aren't you supposed to be watching television or something? "We'll be late," he says. "We will be late. For what? "For the overnight hike!" he says. "Remember? You promised me I could volunteer you to go along and help the troop-master. "I mutter something no Boy Scout should ever hear. But Dave isn't fazed. "Come on. Just get in the shower," he says, as he pulls me out of bed. "I packed your gear last night. Everything's in the car already. We just have to get there by eight. "I manage a last look at Julie, her eyes still shut, and the warm soft mattress as Davey drags me through the door. An hour and ten minutes later, my son and I arrive at the edge of some forest. Waiting for us is the troop: fifteen boys outfitted in caps, neckerchiefs, merit badges, the works. Before I have time to say, "Where's the troop master?", the other few parents who happen to be lingering with the boy's takeoff in their cars, all pedals to the metal. Looking around, I see that I am the only adult in sight. "Our troop master couldn't make it," says one of the boys. "How come? "He's sick," says another kid next to him. "Yeah, his hemorrhoids are acting up," says the first. "So, it looks like you're in charge now. "What are we supposed to do, Mr. Rogo?" asks the other kid. Well, at first, I'm a little mad at having all this foisted upon me. But then the idea of having to supervise a bunch of kids doesn't daunt meafter all, I do that every day at the plant. So, I gather everyone around. We look at a map and discuss the objectives for this expedition into the perilous wilderness before us The plan, I learn, is for the troop to hike through the forest following a blazed trail to someplace called "Devil's Gulch." There we are to bivouac for the evening. In the morning we are to break camp and make our way back to the point of departure, where Mom and Dad are supposed to be waiting for little Freddy and Johnny and friends to walk out of the woods. First, we have to get to Devil's Gulch, which happens to be about ten miles away. So I line up the troop. They've all got their rucksacks on their backs. Map in hand, I put myself at the front of the line in order to lead the way, and off we go. The weather is fantastic. The sun is shining through the trees. The skies are blue. It's breezy and the temperature is a little on the cool side, but once we get into the woods, it's just right for walking. The trail is easy to follow because there are blazes (splotches of yellow paint) on the tree trunks every 10 yards or so. On either side, the undergrowth is thick. We have to hike in single file. I suppose I'm walking at about two miles per hour, which is about how fast the average person walks. At this rate, I think to myself, we should cover ten miles in about five hours. My watch tells me it's almost 8:30 now. Allowing an hour and a half forbreaks and for lunch, we should arrive at Devil's Gulch by three o'clock, no sweat. After a few minutes, I turn and look back. The column of scouts has spread out to some degree from the close spacing we started with. Instead of a yard or so between boys, there are now larger gaps, some a little larger than others. I keep walking. But I look back again after a few hundred yards, and the column is stretched out much farther. And a couple of big gaps have appeared. I can barely see the kid at the end of the line. I decide it's better if I'm at the end of the line instead of at the front. That way I know I'll be able to keep an eye on the whole column, and make sure nobody gets left behind. So I wait for the first boy to catch up to me, and I ask him his name. "I'm Ron," he says. "Ron, I want you to lead the column," I tell him, handing over the map. "Just keep following this trail and set a moderate pace. Okay? "Right, Mr. Rogo." And he sets off at what seems to be a reasonable pace "Everybody stay behind Ron!" I call back to the others. "Nobody passes Ron, because he's got the map. Understand? "Everybody nods, waves. Everybody understands. I wait by the side of the trail as the troop passes. My son, Davey, goes by talking with a friend who walks close behind him. Now that he's with his buddies, Dave doesn't want to know me. He's too cool for that. Five or six more come along, all of them keeping up without any problems. Then there is a gap, followed by a couple more scouts. After them, another, even larger gap has occurred. I look down the trail. And I see this fat kid. He already looks a little winded. Behind him is the rest of the troop. "What's your name?" I ask as the fat kid draws closer. "Herbie," says the fat kid. "You okay, Herbie? "Oh, sure, Mr. Rogo," says Herbie. "Boy, it's hot out, isn't it?" Herbie continues up the trail and the others follow. Some of them look as if they'd like to go faster, but they can't get around Herbie. I fall in behind the last boy. The line stretches out in front of me, and most of the time, unless we're going over a hill or around a sharp bend in the trail, I can see everybody. The column seems to settle into a comfortable rhythm. Not that the scenery is boring, but after a while I begin to think about other things. Like Julie, for instance. I really had wanted to spend this weekend with her. But I'd forgotten all about this hiking business with Dave. "Typical of you," I guess she'd say. I don't know how I'm ever going to get the time I need to spend with her. The only saving grace about this hike is that she ought to understand I have to be with Dave. And then there is the conversation I had with Jonah in New York. I haven't had any time to think about that. I'm rather curious to know what a physics teacher is doing riding around in limousines with corporate heavyweights. Nor do I understand what he was trying to make out of those two items he described. I mean, "dependent events" . . . "statistical fluctuations"so what? They're both quite mundane. Obviously, we have dependent events in manufacturing. All it means is that one operation has to be done before a second operation can be performed. Parts are made in a sequence of steps. Machine A has to finish Step One before Worker B can proceed with Step Two. All the parts have to be finished before we can assemble the product. The product has to be assembled before we can ship it. And so on. But you find dependent events in any process, and not just those in a factory. Driving a car requires a sequence of dependent events. So does the hike we're taking now. In order to arrive at Devil's Gulch, a trail has to be walked. Up front, Ron has to walk the trail before Davey can walk it. Davey has to walk the trail before Herbie can walk it. In order for me to walk the trail, the boy in front of me has to walk it first. It's a simple case of dependent events. And statistical fluctuations? I look up and notice that the boy in front of me is going a little faster than I have been. He's a few feet farther ahead of me than he was a minute ago. So I take some bigger steps to catchup. Then, for a second, I'm too close to him, so I slow down. There: if I'd been measuring my stride, I would have re-corded statistical fluctuations. But, again, what's the big deal? If I say that I'm walking at the rate of "two miles per hour," I don't mean I'm walking exactly at a constant rate of two miles per hour every instant. Sometimes I'll be going 2.5 miles per hour; sometimes maybe I'll be walking at only 1.2 miles per hour. The rate is going to fluctuate according to the length and speed of each step. But over time and distance, I should be averaging about two miles per hour, more or less. The same thing happens in the plant. How long does it take to solder the wire leads on a transformer? Well, if you get out your stopwatch and time the operation over and over again, you might find that it takes, let's say, 4.3 minutes on the average. But the actual time on any given instance may range between 2.1minutes up to 6.4 minutes. And nobody in advance can say, "This one will take 2.1 minutes . . . this one will take 5.8 minutes. "Nobody can predict that information. So what's wrong with that? Nothing as far as I can see. Any- way, we don't have any choice. What else are we going to use in place of an "average" or an "estimate"? I find I'm almost stepping on the boy in front of me. We've slowed down somewhat. It's because we're climbing a long, fairly steep hill. All of us are backed up behind Herbie. "Come on, Herpes!" says one of the kids. Herpes? "Yeah, Herpes, let's move it," says another.

"Okay, enough of that," I say to the persecutors. Then Herbie reaches the top. He turns around. His face is red from the climb. "Atta boy, Herbie!" I say to encourage him. "Let's keep it moving! "Herbie disappears over the crest. The others continue the climb, and I trudge behind them until I get to the top. Pausing there, I look down the trail. Holy cow! Where's Ron? He must be half a mile ahead of us. I can see a couple of boys in front of Herbie, and everyone else is lost in the distance. I cup my hands over my mouth. "HEY! LET'S GO UP THERE! LET'S CLOSE RANKS!" I yell. "DOUBLE TIME! DOUBLE TIME! "Herbie eases into a trot. The kids behind him start to run. I jog after them. Rucksacks and canteens and sleeping bags are bouncing and shaking with every step. And HerbieI don't know what this kid is carrying, but it sounds like he's got a junk-yard on his back with all the clattering and clanking he makes when he runs. After a couple hundred yards, we still haven't caught up. Herbie is slowing down. The kids are yelling at him to hurry up. I'm huffing and puffing along. Finally, I can see Ron off in the distance. "HEY RON!" I shout. "HOLD UP!" The call is relayed up the trail by the other boys. Ron, who probably heard the call the first time, turns and looks back. Herbie, seeing relief in sight, slows to a fast walk. And so do the rest of us. As we approach, all heads are turned our way. "Ron, I thought I told you to set a moderate pace," I say. "But I did!" he protests. "Well, let's just all try to stay together next time," I tell them. "Hey, Mr. Rogo, what'd say we take five?" asks Herbie. "Okay, let's take a break," I tell them. Herbie falls over beside the trail, his tongue hanging out. Everyone reaches for canteens. I find the most comfortable log insight and sit down. After a few minutes, Davey comes over and sits down next to me. "You're doing great, Dad," he says. "Thanks. How far do you think we've come? "About two miles," he says. "Is that all?" I ask. "It feels like we ought to be there by now. We must have covered more distance than two miles."

"Not according to the map Ron has," he says. "Oh," I say. "Well, I guess we'd better get a move on." The boys are already lining up. "All right, let's go," I say. We start out again. The trail is straight here, so I can see everyone. We haven't gone thirty yards before I notice it starting all over again. The line is spreading out; gaps between the boys are widening. Dammit, we're going to be running and stopping all day long if this keeps up. Half the troop is liable to get lost if we can't stay together. I've got to put an end to this. The first one I check is Ron. But Ron, indeed, is setting a steady, "average" pace for the troopa pace nobody should have any trouble with. I look back down the line, and all of the boys are walking at about the same rate as Ron. And Herbie? He's not the problem anymore. Maybe he felt responsible for the last de-lay, because now he seems to be making a special effort to keep up. He's right on the ass of the kid in front of him. If we're all walking at about the same pace, why is the distance between Ron, at the front of the line, and me, at the end of the line, increasing? Statistical fluctuations? Nah, couldn't be. The fluctuations should be averaging out. We're all moving at about the same speed, so that should mean the distance between any of us will vary somewhat, but will even out over a period of time. The distance between Ron and me should also expand and contract within a certain range, but should average about the same throughout the hike. But it isn't. As long as each of us is maintaining a normal, moderate pace like Ron, the length of the column is increasing. The gaps between us are expanding. Except between Herbie and the kid in front of him. So how is he doing it? I watch him. Every time Herbie gets a step behind, he runs for an extra step. Which means he's actually expanding more energy than Ron or the others at the front of the line in order to maintain the same relative speed. I'm wondering how long he'll be able to keep up his walk-run routine. Yet . . . why can't we all just walk at the same pace as Ron and stay together? I'm watching the line when something up ahead catches my eye. I see Davey slow down for a few seconds. He's adjusting his pack straps. In front of him, Ron continues onward, oblivious. A gap of ten . . . fifteen . . . twenty feet opens up. Which means the entire line has grown by 20 feet. That's when I begin to understand what's happening. Ron is setting the pace. Every time someone moves slower than Ron, the line lengthens. It wouldn't even have to be as obvious as when Dave slowed down. If one of the boys takes a step that's half an inch shorter than the one Ron took, the length of the whole line could be affected. But what happens when someone moves faster than Ron? Aren't the longer or faster steps supposed to make up for the spreading? Don't the differences average out? Suppose I walk faster. Can I shorten the length of the line? Well, between me and the kid ahead of me is a gap of about five feet. If he continues walking at the same rate, and if I speed up, I can reduce the gapand maybe reduce the total length of the column, depending upon what's happening up ahead. But I can only do that until I'm bumping the kid's rucksack (and if I did that he'd sure as hell tell his mother). So I have to slow down tohis rate. Once I've closed the gap between us, I can't go any faster than the rate at which the kid in front of me is going. And he ultimately can't go any faster than the kid in front of him. And soon up the line to Ron. Which means that, except for Ron, each of our speeds depends upon the speeds of those in front of us in the line. It's starting to make sense. Our hike is a set of dependent events ... in combination with statistical fluctuations. Each of us is fluctuating in speed, faster and slower. But the ability to go faster than average is restricted. It depends upon all the others ahead of me in the line. So even if I could walk five miles per hour, I couldn't do it if the boy in front of me could only walk two miles per hour. And even if the kid directly in front of me could walk that fast, neither of us could do it unless all the boys in the line were moving at five miles per hour at the same time. So I've got limits on how fast I can goboth my own (I can only go so fast for so long before I fall over and pant to death)and those of the others on the hike. However, there is no limit on my ability to slow down. Or on anyone else's ability to slow down. Or stop. And if any of us did, the line would extend indefinitely. What's happening isn't an averaging out of the fluctuations in our various speeds, but an accumulation of the fluctuations. And mostly it's an accumulation of slowness because dependency limits the opportunities for higher fluctuations. And that's why the line is spreading. We can make the line shrink only by having everyone in the back of the line move much faster than Ron's average overcome distance. Looking ahead, I can see that how much distance each of us has to make up tends to be a matter of where we are in the line. Davey only has to make up for his own slower than average fluctuations relative to Ronthat twenty feet or so which is the gap in front of him. But for Herbie to keep the length of the line from growing, he would have to make up for his own fluctuations plus those of all the kids in front of him. And here I am at the end of the line. To make the total length of the line contract, I have to move faster than average for a distance equal to all the excess space between all the boys. I have to make up for the accumulation of all their slowness. Then I start to wonder what this could mean to me on the job. In the plant, we've definitely got both dependent events and statistical fluctuations. And here on the trail we've got both of them. What if I were to say that this troop of boys is analogous toa manufacturing system . . . sort of a model. In fact, the troop does produce a product; we produce "walk trail." Ron begins production by consuming the unwalled trail before him, which is the equivalent of raw materials. So Ron processes the trail first by walking over it, then Davey has to process it next, followed by the boy behind him, and so on back to Herbie and the others and onto me. Each of us is like an operation which has to be performed to produce a product in the plant; each of us is one of a set of dependent events. Does it matter what order we're in? Well, somebody has to be first and somebody else has to be last. So we have dependent events no matter if we switch the order of the boys. I'm the last operation. Only after I have walked the trail is the product "sold," so to speak. And that would have to be our throughputnot the rate at which Ron walks the trail, but the rate at which I do. What about the amount of trail between Ron and me? It has to be inventory. Ron is consuming raw materials, so the trail the rest of us are walking is inventory until it passes behind me. And what is operational expense? It's whatever lets us turn inventory into throughput, which in our case would be the energy the boys need to walk. I can't really quantify that for the model, except that I know when I'm getting tired. If the distance between Ron and me is expanding, it can only mean that inventory is increasing. Throughput is my rate of walking. Which is influenced by the fluctuating rates of the others. Hmmm. So as the slower than average fluctuations accumulate, they work their way back to me. Which means I have to slowdown. Which means that, relative to the growth of inventory, throughput for the entire system goes down. And operational expense? I'm not sure. For UniCo, when-ever inventory goes up, carrying costs on the inventory go up as well. Carrying costs are a part of operational expenses, so that measurement also must be going up. In terms of the hike, operational expense is increasing any time we hurry to catch up, be-cause we expend more energy than we otherwise would. Inventory is going up. Throughput is going down. And operational expense is probably increasing. Is that what's happening in my plant? Yes, I think it is. Just then, I look up and see that I'm nearly running into the kid in front of me. Ah ha! Okay! Here's proof I must have overlooked some-thing in the analogy. The line in front of me is contracting rather than expanding. Everything must be averaging out after all. I'm going to lean to the side and see Ron walking his average two-mile-an-hour pace. But Ron is not walking the average pace. He's standing still at the edge of the trail. "How come we're stopping? "He says, "Time for lunch, Mr. Rogo."

QUESTION:

What did Al learn about productivity from 'the hike?